## Understanding (7/8)^-1

In mathematics, a negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. Let's break down what this means for (7/8)^-1:

### Reciprocals

The reciprocal of a number is simply 1 divided by that number. For example, the reciprocal of 5 is 1/5.

### Applying the Rule

Applying the rule of negative exponents to (7/8)^-1, we get:

(7/8)^-1 = 1 / (7/8)^1

Since any number raised to the power of 1 is itself, we have:

1 / (7/8)^1 = 1 / (7/8)

### Calculating the Result

To divide by a fraction, we multiply by its reciprocal. The reciprocal of (7/8) is (8/7). Therefore:

1 / (7/8) = 1 * (8/7) = 8/7

### Conclusion

Therefore, **(7/8)^-1 is equal to 8/7**. This demonstrates how understanding negative exponents allows us to simplify complex expressions and arrive at a straightforward solution.